Continent-based games are tricky. When I find myself unable to conquer my neighbours, I try to Chop + Whip Libraries in 3 different Cities which each have at least a 5-Food Resource and preferably another 3-Food square to work. Then, I regrow those 3 Cities to Size 4 and hire 2 Scientist Specialists in each.
The third Great Person requires 300 Great People Points (GPP) on Normal Game Speed, meaning that if I hire 2 Scientist Specialists in a City, making 3 GPP each, that's 2 Scientists * 3 GPP = 6 GPP per turn. 300 GPP / 6 GPP per turn = 50 turns.
So, it's a matter of getting Writing and Bronze Working early enough, getting up a few decent Cities, and then it comes down to the timing of when that last City starts hiring its 2 Scientist Specialists as to when to start the 50-turn countdown.
If my capital has a lot of Commerce, say, with Rivers and Commerce-based Resources, I'll use the first Great Scientist on an Academy in my capital. Otherwise, I will save it for Lightbulbing Optics. The other 2 Great Scientists get saved for Lightbulbing Astronomy.
For Optics, you'll need Sailing, Metal Casting, Machinery, Iron Working, and Compass, as well as Mathematics and Alphabet due to Mathematics and Alphabet being higher priorities for a Great Scientist to Lightbulb. For Astronomy, you'll also need Calendar.
Optics can let you meet overseas AIs before they come to meet you--whoever does the meeting first tends to be the one to get the most technology trades. Try not to trade away Optics and Astronomy. If you have Galleons from Astronomy, even a technologically backward army of yours can help you to take advantage of an overseas AI, as you can land some stacks of troops to capture and hold a couple of an AI's poorly-defended Cities by picking AI Cities that are poorly-defended. You can also steal Workers that are next to the coast if an AI hasn't already improved the land on your behalf.
Assuming that you don't have newer technologies, bring along 1 Archer, 2 Spearman, and 1 Axeman to defend a captured City, in addition to your attacking Units. There are other tactics that you can use, such as landing your stack on a Hills Forest square and hoping that the AI will attack your stack of Units with their stack of Units, but it's not always easy to do so. Your attacking stack will hopefully consist of 15 Units, so that even if you just have Axemen and Swordsmen, you'll have enough numbers to capture a good City or two. Preferably, you'll have also brought along some Catapults, if you've managed to also research Construction, but Catapults can also come in the second wave of attackers.
The goal is to capture a good City or two and then get a Peace Treaty. Since you should have been able to trade for techs, even if you lost more Units than you killed, you can give away a tech to get Peace. Since you didn't focus on building World Wonders, it's a great time to try to capture an overseas City with a good World Wonder in it, such as The Great Lighthouse or The Pyramids, or to capture a City that already has a Holy Shrine in it--which is more likely to occur when you let the AIs build Stonehenge and The Oracle instead of trying to build World Wonders yourself while also hiring so many Scientist Specialists, which isn't a reliable approach if you haven't already dominated your own continent's AIs.
Your new overseas holdings can be used to whip out more Military Units while your home continent Cities also build more Military Units and Galleons. Keep building up a large attack force and bring along some defensive Units and then start another war to capture another good City or two from another overseas AI.
When you first meet an AI, if you trade it a tech, it will give you +4 Diplo Attitude bonus for Fair and Forthright Trading, but you might also incur a -4 Diplo Attitude penalty with any AI who has met that AI and who treats that AI as their Worst Enemy. So, it can be worth holding off on tech trading until you've met at least a couple of AIs on the same continent as each other, just to get a feel for which AI is someone else's Worst Enemy and then can decide whether to trade with that AI or not.
Depending upon which AIs you meet, it may sometimes be possible to declare war on one AI and then bribe another AI into war with the first AI, to provide a distraction for both of their armies. Doing so can backfire as the AI that you bribed into the war may build more military troops than it otherwise would have and those troops may not get sent into battle. If you can instead bribe AIs to Stop Trading with each other, that approach might be preferable, just to avoid losing your captured Cities from the first war (which you are still defending, so it shouldn't be too much of a problem anyway, right?) to the second AI on which you declare war due to the AI on whom you declared war second having Open Borders with the AI on whom you declared war on first.
Basically, try to launch some short wars with a lot of force being packed into a single location at once thanks to the help of your Galleons and focus on capturing the valuable Cities--ones with World Wonders, Holy Shrines, or Happiness Resources, then leave your captured Cities defended with a decent garrison to prevent losing those Cities easily.
AIs are not well-equipped to handle naval warfare and if you are playing a map with a Cylindrical World Wrap or Toroidal World Wrap (meaning not a Flat World Wrap that represents just a small portion of the world), you should be able to get the Circumnavigation bonus yourself. Even without that bonus, Galleons can move 4 squares per turn. AIs are great at watching your army march over land toward their Cities and then being prepared when your army arrives at that AI's Cities' doorsteps, but when you can land your troops next to the doorstep of one of the AI's best Cities on the first turn of war, you'll be catching that AI with its pants down.
You can also choose which AI to attack first, due to the maneuverability of your Galleons, meaning that if one AI already has Feudalism and Longbowmen, you can optionally skip that AI if your initial army doesn't have Catapults and instead go for a softer AI target until your second wave of attackers arrives, which should come with Catapults, as you'll have had enough time to have researched Construction by then.
With Lightbulbing Astronomy, and with you not trading away Optics and Astronomy, it will be a while before the AIs can build a fleet of their own, meaning only the Cities that you capture overseas will be vulnerable to counter-attack. If you've been friendly with your home continent's neighbours, they hopefully won't backstab you, and the fact that you increased your military Power will also deter them from attacking you--an AI doesn't calculate the fact that your army is far overseas and will still give you full "credit" for your military Power, regardless of where the Units are currently stationed in the world.
This strategy is about getting to Astronomy first, well ahead of the AIs. If you get to Astronomy later, it can still work, but you'll likely need Catapults and/or Trebuchets and a better army than just a large stack of Axemen plus a few mixed City Defenders for your first wave of attack, meaning that the timing of hiring your third City's worth of 2 Scientist Specialists is the key timing factor.
Also, you'll want to avoid learning one of Meditation until after you have Lightbulbed Astronomy, so that Philosophy doesn't come up as the Lightbulb option in place of Astronomy. If you accidentally learn Meditation, say, by getting it in trade or simply forgetting, then you'll need to avoid both of Code of Laws and Drama until after you have learned Astronomy.
Similarly, you'll want to avoid learning both of Theology and Civil Service until after you have Lightbulbed Astronomy, so that Paper doesn't come up as the Lightbulb option in place of Astronomy.
If you do have access to Iron, then you could instead make the stack of Units which will defend a captured City be 2 Crossbowmen and 1 Spearman.
The biggest keys are getting your 3 Scientist-specialist Cities started, not taking technologies in trade that will alter the Great Scientist Lightbulbing preferences away from Astronomy, and then planning out your whipping of Galleons and troops so that you can go in with roughly 6 Galleons full of Units to ensure that you can capture and hold your targeted overseas AI City. Get the good Cities first, defend them, make Peace, and then whip more troops from captured Cities, whip more troops at home, and get ready for the next assault on a different overseas AI victim.
Over time, you'll be capturing the AIs' best Cities and then defending them (you can whip City Walls, too, once those Cities come out of City Revolt), and you'll be using your homeland Cities to pump out a steady stream of troops without the need to really defend your homeland Cities.
Remember, the technological advantage is your friend--once an AI is willing to talk with you after several turns of war, it's just a matter of paying a tech to get out of a war that isn't currently going your way.
As for capturing AI works from the sea, be sure to land 2 or more troops on a captured Worker, as an AI will very happily counter-attack a single Unit of yours that steals its Worker this way, but the AI will think twice about attacking when you land 2 or 3 troops just to capture a Worker. After you've captured a key City or two and are able to defend that City or those Cities, excess surviving attacking troops can grab Workers in this way (landing from Galleons) while you wait for the AI to be willing to talk with you and sign a Peace Treaty, all while you're building up more troops for your next AI invasion.
If you own an AI's good Cities, then as you get more technologies, you can better defend those Cities from counter-attack over time, but the key is to get those Cities when it's easy to capture them and then hold onto them, so that the player defending those Cities as technologies get learned world-wide and defending Units' technologies increase ends up being you, rather than an AI, so that you can get the easy City captures and the AIs will then be the ones complaining that it's too hard to capture the well-defended Cities.
Sure, players who happen to dominate their own continent may not need to resort to these tactics, since, in a continents game, dominating one's continent early on does give a lot more options, but I find that it's not always possible or not always preferable to beat up on my nearby neighbours, leaving this 3-Library-plus-2-Scientist-Specialists-per-Library-City approach as a way to get yourself back into the game in a tactically advantageous way.
Sure, other options also exist, such as avoiding learning Meditation, learning Code of Laws relatively early on, and using Caste System to hire Scientist Specialists, but that's getting into more advanced tactics that will work better on maps with a decent amount of Happiness Resources and a City or two with 3+ Food Resources to be able to hire a lot of Scientist Specialists from one or two Cities without the need for Libraries... it's nice to hope for such a case, but it's not a tactic that you can always depend on.
